After examining the cable and finding the location of the cut, I decide do try fixing it in place by adding a couple of short patch wires.
This is what I had to work with...
I untwisted the orange/orange-white cable pair and soldered on two short length of wire, connecting the two cables back. Surprisingly the light for the network cable on the router came back on. I had connectivity again!
Testing transfer speeds with this patch gave good results as well - doesn't look like the patch is causing any/much signal interference or loss.
Finally I added shifted the heat shrink over to cover the exposed wires, shrank it and sealed everything with electrical tape.
This patch seems to work, this is in no way a professional fix, though it means I can keep using a wired network from my server to the router.